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Bending of trajectories in general relativity by a tidal force
called a geodesic. The geodesic deviation equation relates the Riemann curvature tensor to the relative acceleration of two neighboring geodesics. In differential
Geodesic_deviation
Equations that describe the behavior of a physical system
force. The relative acceleration of one geodesic to another in curved spacetime is given by the geodesic deviation equation: D 2 ξ α d s 2 = − R α β γ δ
Equations_of_motion
Mathematical theory of the geometry of space and time
measurements made entirely within spacetime itself of such effects as geodesic deviation and tidal effects (described above in the Introduction). In relativistic
Curved_spacetime
Tensor field in Riemannian geometry
observable via the geodesic deviation equation. The curvature tensor represents the tidal force experienced by a rigid body moving along a geodesic in a sense
Riemann_curvature_tensor
Plane curved by the intersection of an earth ellipsoid and a plane
computed. This distance is described as the lateral deviation from the geodesic, or briefly geodesic deviation, and is displayed in the charts on the right.
Earth_section_paths
used to describe how initially parallel geodesics diverge. This is expressed by the equation of geodesic deviation and means that the tidal forces experienced
Mathematics of general relativity
Mathematics_of_general_relativity
Vector field in Riemannian geometry
a geodesic γ {\displaystyle \gamma } in a Riemannian manifold describing the difference between the geodesic and an "infinitesimally close" geodesic. In
Jacobi_field
Mathematics of smooth surfaces
a geodesic of sufficiently short length will always be the curve of shortest length on the surface which connects its two endpoints. Thus, geodesics are
Differential geometry of surfaces
Differential_geometry_of_surfaces
Solution to the Einstein field equations
thus the components do not change for non-static observers. The geodesic deviation equation shows that the tidal acceleration between two observers separated
Schwarzschild_metric
Fundamental concept of classical mechanics
respect to each other will continue to do so. This phenomenon of geodesic deviation means that inertial frames of reference do not exist globally as they
Inertial_frame_of_reference
Frame-dependent apparent force in Physics
Stephani (2004). Introduction to Special and General Relativity - geodesic deviation p. 104-105. Cambridge UK: Cambridge University Press. p. 105. ISBN 0-521-01069-1
Fictitious_force
Field variables
were to reconstruct the Riemann curvature tensor by measurements of geodesic deviation, we would in fact obtain the curvature tensor in the Jordan frame
Jordan_and_Einstein_frames
1957 international physics conference
first time how to mathematically treat gravitational waves using the geodesic deviation introduced by John Lighton Synge. He showed how two masses would move
Chapel_Hill_Conference
Field-equations in general relativity
squares of deviations from the Minkowski metric are negligible. Applying these simplifying assumptions to the spatial components of the geodesic equation
Einstein_field_equations
parallelism Prime geodesic Geodesic flow Exponential map (Lie theory) Exponential map (Riemannian geometry) Injectivity radius Geodesic deviation equation Jacobi
List of differential geometry topics
List_of_differential_geometry_topics
Paths of particles in the Schwarzschild solution to Einstein's field equations
In general relativity, Schwarzschild geodesics describe the motion of test particles in the gravitational field of a central fixed mass M , {\textstyle
Schwarzschild_geodesics
Science of measuring the shape, orientation, and gravity of Earth
The general solution is called the geodesic for the surface considered, and the differential equations for the geodesic are solvable numerically. On the
Geodesy
Detail of the global positioning system
individual components (i.e., RSS for root sum squares). To get the standard deviation of receiver position estimate, these range errors must be multiplied by
Error analysis for the Global Positioning System
Error_analysis_for_the_Global_Positioning_System
Notion for convergence of metric spaces
complete, and separable. It is also geodesic, i.e., any two of its points are the endpoints of a minimizing geodesic. In the global sense, the Gromov–Hausdorff
Gromov–Hausdorff_convergence
Mesyats Geocentric model Geocentric orbit Geodesic Geodesic deviation equation Geodesics as Hamiltonian flows Geodesics in general relativity Geodetic effect
Index_of_physics_articles_(G)
Algorithm used to solve non-linear least squares problems
step as the velocity v k {\displaystyle {\boldsymbol {v}}_{k}} along a geodesic path in the parameter space, it is possible to improve the method by adding
Levenberg–Marquardt_algorithm
Main body of an aircraft
covering to form a more aerodynamic shape, or one more pleasing to the eye. Geodesic structural elements were used by Barnes Wallis for British Vickers between
Fuselage
19th-century survey to measure the Indian subcontinent
measurements of a section of an arc of longitude, and for measurements of the geodesic anomaly, which led to the development of the theories of isostasy. The
Great_Trigonometrical_Survey
Product of the principal curvatures of a surface
is called the total curvature. The total curvature of a geodesic triangle equals the deviation of the sum of its angles from π. The sum of the angles of
Gaussian_curvature
Russian mathematician (born 1962)
2006 International Congress of Mathematicians in Madrid. The theme was: "Geodesics on flat surfaces". At least two of his papers concern the explanation
Anton_Zorich
Architectural element similar to the hollow upper half of a sphere; there are many types
designed many geodesic domes and patented them in the United States. Geodesic dome in Jena, Germany Geodesic dome of the Montreal Biosphere Geodesic dome home
Dome
Schwarzschild solution; the motion is a geodesic ("shortest path between two points") in the curved space-time. Such geodesic solutions account for the anomalous
Two-body problem in general relativity
Two-body_problem_in_general_relativity
[citation needed] If initially parallel paths of two particles on nearby geodesics remain parallel within some accuracy, then spacetime is flat to within
Newtonian motivations for general relativity
Newtonian_motivations_for_general_relativity
theoretical motivation for general relativity, including the motivation for the geodesic equation and the Einstein field equation, can be obtained from special
Theoretical motivation for general relativity
Theoretical_motivation_for_general_relativity
Rotation of Earth around its axis
orientation parameters Formation and evolution of the Solar System Geodesic (in mathematics) Geodesics in general relativity Geodesy History of Earth History of
Earth's_rotation
Distinguished surfaces of dynamic trajectories
null-geodesics of appropriate metric tensors defined by the deformation field—hence the name of this theory. Shearless LCSs are found to be null-geodesics
Lagrangian_coherent_structure
spheroid. This dispute raged until the French Geodesic Mission to the Equator of 1735-1751 and the French Geodesic Mission to Lapland of 1736–1737 decided the
Timeline_of_Earth_estimates
Fastest curve descent without friction
problem at MacTutor Geodesics Revisited — Introduction to geodesics including two ways of derivation of the equation of geodesic with brachistochrone
Brachistochrone_curve
Classical statement of gravity as force
gravitational acceleration of a body in free fall is due to its world line being a geodesic of spacetime. In recent years, quests for non-inverse square terms in the
Newton's law of universal gravitation
Newton's_law_of_universal_gravitation
Theory of gravitation as curved spacetime
particular type of geodesic in curved spacetime. In other words, a freely moving or falling particle always moves along a geodesic. The geodesic equation is:
General_relativity
Size and shape used to model the Earth for geodesy
the Earth (radius and circumference) Geodetic coordinates Geodetic datum Geodesic Horizontal position representation Latitude / Longitude Map projection
Figure_of_the_Earth
Geometric mean and hyperbolic angle as coordinates in quadrant I
notion of hyperbolic motions. Since geodesics in HP are semicircles with centers on the boundary, the geodesics in Q are obtained from the correspondence
Hyperbolic_coordinates
Deviation from Kepler's third law
In physics, the gravitomagnetic clock effect is a deviation from Kepler's third law that, according to the weak-field and low-velocity approximation of
Gravitomagnetic_clock_effect
Hypothetical quantum cosmological effect
are functions of frequency and angular momentum that characterize the deviation of the emission-spectrum of a black hole from a pure black-body spectrum
Hawking_radiation
Providing control of layout during building
and surveys of existing conditions are generally performed according to geodesic coordinates. However, for the purposes of construction a more suitable
Construction_surveying
Predecessor to the theory of relativity
free test particle is a timelike geodesic, and by an obvious limit, the world line of a laser pulse is a null geodesic), but we lose the conservation law
Nordström's theory of gravitation
Nordström's_theory_of_gravitation
Satellite inflated with gas after being put into orbit
even larger 40-meter (130 ft) balloon Pageos. The name is from "passive geodesic satellite", and sounds similar to "Geos", a successful active electronic
Balloon_satellite
Physical law
square of the distance between them; this is known as Coulomb's law. The deviation of the exponent from 2 is less than one part in 1015. F = k e q 1 q 2
Inverse-square_law
Mechanical structure of an aircraft
Mitchell and P-38 Lightning, and British Vickers Wellington that used a geodesic construction method, and Avro Lancaster, all revamps of original designs
Airframe
Measured time difference as explained by relativity theory
nanoseconds during the westward trip (where the error bars represent standard deviation). In 2005, the National Physical Laboratory in the United Kingdom reported
Time_dilation
Computer vision framework
constant. A more sophisticated deformable model formulation that combines the geodesic active contour flow with GVF forces was proposed in . This paper also shows
Gradient_vector_flow
German polymath and scholar (1777–1855)
triangles to geodesic triangles on arbitrary surfaces with continuous curvature; he found that the angles of a "sufficiently small" geodesic triangle deviate
Carl_Friedrich_Gauss
Main structural member of the wing of an aircraft
wing structural integrity. In aircraft such as the Vickers Wellington, a geodesic wing spar structure was employed, which had the advantages of being lightweight
Spar_(aeronautics)
Attraction of masses and energy
in spacetime (not 3D space) taken by a free-falling object is called a geodesic and the length of that path as measured by time in the objects frame is
Gravity
Meridian line in Paris, France
equator, the other in a high latitude. Thus arose the celebrated French Geodesic Missions [fr], to the Equator and to Lapland, the latter directed by Pierre
Paris_meridian
Path selection method for aircraft
RNP AR procedures support only two leg types: TF leg: Track to Fix: a geodesic path between two fixes. RF leg: Radius to Fix. This is a curved path supported
Required navigation performance
Required_navigation_performance
Theory of gravity by Albert Einstein
properties of geodesics differ from those of straight lines. For example, on a plane, parallel lines never meet, but this is not so for geodesics on the surface
Introduction to general relativity
Introduction_to_general_relativity
Motion of a body subject only to gravity
free fall is subject to no force and is an inertial body moving along a geodesic. Far away from any sources of space-time curvature, where spacetime is
Free_fall
Line between the poles with the same longitude
magnetic meridian, because of the longitude from east to west being complete geodesic. The angle between the magnetic and the true meridian is the magnetic declination
Meridian_(geography)
Geodetic survey from 1792 to 1798
called toise of Peru, which had been constructed in 1735 for the French Geodesic Mission to Peru, as well as to Borda's double-toise N°1, one of the four
Arc measurement of Delambre and Méchain
Arc_measurement_of_Delambre_and_Méchain
rule 100-year flood A priori probability Abductive reasoning Absolute deviation Absolute risk reduction Absorbing Markov chain ABX test Accelerated failure
List_of_statistics_articles
Computer vision framework
different training data sets and tunings. Geometric active contour, or geodesic active contour (GAC) or conformal active contours employs ideas from Euclidean
Active_contour_model
Geometric figure which approximates the Earth's shape
defined. In the context of standardization and geographic applications, a geodesic reference ellipsoid is the mathematical model used as foundation by spatial
Earth_ellipsoid
Ocean shape without winds and tides
+8,800 m (Mount Everest) and −11,000 m (Marianas Trench), the geoid's deviation from an ellipsoid ranges from +85 m (Iceland) to −106 m (southern India)
Geoid
Speed of electromagnetic waves in vacuum
History of measurements of c (in m/s) Year Experiment Value Deviation from 1983 value <1638 Galileo, covered lanterns inconclusive <1667 Accademia del
Speed_of_light
2015 European Space Agency spacecraft
external forces acting on the test masses, guaranteeing small deviations from geodesic motion, and to measure their relative displacement with high precision
LISA_Pathfinder
Hypothesis that inertial and gravitational masses are equivalent
objects. Highly precise experimental tests of the principle limit possible deviations from equivalence to be very small. In classical mechanics, Newton's equation
Equivalence_principle
Conjecture on zeros of the zeta function
an infinite product similar to the Euler product but taken over closed geodesics rather than primes. The Selberg trace formula is the analogue for these
Riemann_hypothesis
Number, approximately 3.14
density function of the normal distribution with mean μ and standard deviation σ, naturally contains π: f ( x ) = 1 σ 2 π e − ( x − μ ) 2 / ( 2 σ 2 )
Pi
Array of numbers
roughly speaking, numerically stable if little deviations in the input values do not lead to big deviations in the result. For example, one can calculate
Matrix_(mathematics)
GIS databases. geodesic In geodesy, the shortest line on a specific surface between two particular points on that surface. The geodesic between a given
Glossary of geography terms (A–M)
Glossary_of_geography_terms_(A–M)
Chemistry of carbon's allotrope fullerene
50 mg of Au/CD captures 5 mg of C60 fullerene. Solubility of fullerenes Geodesic polyarene Hirsch, A.; Bellavia-Lund, C., eds. (1993). Fullerenes and Related
Fullerene_chemistry
S2CID 8447495. Kahn, Jeremy; Markovic, Vladimir (2012). "Immersing almost geodesic surfaces in a closed hyperbolic three manifold". Annals of Mathematics
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Method of data analysis
projecting the points onto it. See also the elastic map algorithm and principal geodesic analysis. Another popular generalization is kernel PCA, which corresponds
Principal_component_analysis
Direction that Muslims face while praying salah
ellipsoidal models to calculate the qibla, replacing the great circle by the geodesics on an ellipsoid. This results in more complicated calculations, while
Qibla
Trace radiation from the early universe
isotropic mean temperature of the CMB, Tγ = 2.7255±0.0006 K with one standard deviation confidence. This term must be measured with absolute temperature devices
Cosmic_microwave_background
Light bending by mass between source and observer
reluctantly published the short article "Lens-Like Action of a Star By the Deviation of Light In the Gravitational Field" in the journal Science. In 1937,
Gravitational_lens
Study of the physical properties of the Earth's gravity field
deviations from the theoretical gravity of an idealized, smooth Earth ellipsoid. The deviations toward stronger gravity are colored red; deviations toward
Physical_geodesy
relativity in the weak gravitational field limit, severely limiting possible deviations from the theory. In the 1970s, scientists began to make additional tests
Tests_of_general_relativity
Map projection system
value of each depends on the latitude ϕ {\displaystyle \phi } and the deviation in longitude Δ λ = λ − λ 0 {\displaystyle \Delta \lambda =\lambda -\lambda
Universal Transverse Mercator coordinate system
Universal_Transverse_Mercator_coordinate_system
such that f(tx + (1 − t)y) ≤ max(f(x), f(y)) for t ∈ [0,1] Subderivative Geodesic convexity — convexity for functions defined on a Riemannian manifold Duality
List of numerical analysis topics
List_of_numerical_analysis_topics
Hotel in Seattle
is modeled after The Aviary, a cocktail bar in Chicago. The bar has a geodesic dome area called the Rain Drop, which began operations in July 2023 and
Thompson_Seattle
Partial differential equation
boundary is totally geodesic, the solution to the flow converges to a metric of constant positive curvature and totally geodesic boundary. Simon Brendle
Ricci_flow
1972 book by Deleuze and Guattari
Massumi, Brian. 1992. A User's Guide to Capitalism and Schizophrenia: Deviations from Deleuze and Guattari. Swerve editions. Cambridge, United States and
Anti-Oedipus
German astronomer and mathematician (1784–1846)
Bessel, F. W. (2010). "The calculation of longitude and latitude from geodesic measurements". Astronomische Nachrichten. 333 (8). Translated by Ch. F
Friedrich_Wilhelm_Bessel
Measure of phase coupling in a signal
Observation of coherent bicoherence and biphase in potential fluctuations around geodesic acoustic mode frequency on JFT-2M. Plasma Physics and Controlled Fusion
Bicoherence
Quantitative study of size and shape
landmark to the centroid. The configuration is rotated to minimize the deviation between it and a reference, typically the mean shape. In the case of semi-landmarks
Morphometrics
Method of analysis applied to problems wave propagation
reflection and refraction using this principle, but could not explain the deviations from rectilinear propagation that occur when light encounters edges, apertures
Huygens–Fresnel_principle
American satellite-based radio navigation service
to compute four unknown quantities (three position coordinates and the deviation of its own clock from satellite time). Each GPS satellite continually
Global_Positioning_System
Property of certain dynamical systems
chaotic systems, where small changes in initial conditions create wild deviations in the phase space behavior of solutions. Three features are often referred
Integrable_system
named after Richard Buckminster Fuller due to its resemblance to Fuller's geodesic domes. The term was coined by Harold Kroto. The alternative name footballene
List of chemical compounds with unusual names
List_of_chemical_compounds_with_unusual_names
Science of determining the positions of points and the distances and angles between them
measurements of a section of an arc of longitude, and for measurements of the geodesic anomaly. It named and mapped Mount Everest and the other Himalayan peaks
Surveying
Restrictions on using GPS in China
April 2015). "ChinaMapDeviation". GitHub. Archived from the original on 7 April 2015. Guilbot, Maxime (28 May 2013). "ChinaMapDeviation". GitHub. Wu, Yongzheng
Restrictions on geographic data in China
Restrictions_on_geographic_data_in_China
Aspect of relativity in physics
time of arrival of pulses to a telescope, in other words, to look for deviations in the clock ticks. To detect GWs, pulsar timing arrays search for a distinct
Gravitational_wave
light microscopy images. This reconstruction is used for quantifying the geodesic distances between trichomes and their patterning, which is a marker of
Elastic_map
Angle between two objects
The difference between a magnetic bearing and a compass bearing is the deviation caused to the compass by ferrous metals and local magnetic fields generated
Bearing_(navigation)
Physical acceleration experienced by an object
they let go, causing them to fly off along a zero proper-acceleration (geodesic) path. Unaccelerated observers, of course, in their frame simply see their
Proper_acceleration
Signals broadcast by GPS satellites
the variation is higher. The code frequency deviation is 1/1,540 times the carrier frequency deviation for L1 because the code frequency is 1/1,540 of
GPS_signals
Motion of a curve based on its curvature
mean that every compact set has a compact convex hull, as defined using geodesic convexity. The curve-shortening flow cannot cause a curve to depart from
Curve-shortening_flow
Light rays follow quickest paths
Eikonal equation Fermat's and energy variation principles in field theory Geodesic Hamilton's principle Huygens–Fresnel principle Path integral formulation
Fermat's_principle
Theory in physics with scalars and tensors both describing a force or interaction
conservation equation, implying that test-particles follow space-time geodesics such as in general relativity: ∇ σ T μ σ = 0 , {\displaystyle \nabla _{\sigma
Scalar–tensor_theory
System of geographic location identifiers
confidence of 95% or higher". Therefore, the uncertainty is two standard deviations, 2σ, and it is the radius of the disk that represents uncertainty geometrically
Geo_URI_scheme
Branch of mathematics
{\displaystyle A_{\varepsilon }} (the set of points within Euclidean or geodesic distance ε {\displaystyle \varepsilon } from A {\displaystyle A} ) will
Asymptotic_geometry
Curve formed by a hanging chain
the brachistochrone, the circle, and Fermat Unified approach to some geodesics. Ira Freeman "A General Form of the Suspension Bridge Catenary" Bulletin
Catenary
Way of inferring information from cross-covariance matrices
Reinmar J; Tang, Liyao; Guan, Cuntai; Kawanabe, Motoaki (2024). Deep Geodesic Canonical Correlation Analysis for Covariance-Based Neuroimaging Data.
Canonical_correlation
GEODESIC DEVIATION
GEODESIC DEVIATION
GEODESIC DEVIATION
GEODESIC DEVIATION
Girl/Female
Afghan, Arabic, Indian, Kannada, Muslim, Tamil
Safe; Healthy; Mild
Girl/Female
Hindu, Indian, Kannada, Tamil, Telugu
Obedient
Boy/Male
Indian
Actor Power
Boy/Male
Hindu, Indian, Punjabi, Sikh
Child's Plaything
Girl/Female
Greek
Aid.
Girl/Female
Australian, German, Turkish
Lovable
Girl/Female
Indian
Joy, Happiness
Girl/Female
Australian, British, Christian, English, Greek, Latin
Everlasting Life; Name of a Flower
Girl/Female
American, Australian, British, Christian, English, French, Hebrew, Welsh
White Wave; Fair Phantom; Juniper Berry; Form of Geneva; White and Smooth; Soft; Race of Women; White Race
Boy/Male
Italian American
Form of the Latin Marcellus meaning hammer.
GEODESIC DEVIATION
GEODESIC DEVIATION
GEODESIC DEVIATION
GEODESIC DEVIATION
GEODESIC DEVIATION
n.
Same as Geodesy.
a.
Of or pertaining to geodesy; obtained or determined by the operations of geodesy; engaged in geodesy; geodesic; as, geodetic surveying; geodetic observers.
a.
Producing geodes; containing geodes.
n.
That branch of applied mathematics which determines, by means of observations and measurements, the figures and areas of large portions of the earth's surface, or the general figure and dimenshions of the earth; or that branch of surveying in which the curvature of the earth is taken into account, as in the surveys of States, or of long lines of coast.
n.
A geodetic line or curve.
n.
Deviation from the way or proper course.
n.
A moral fault or failing; especially, immoral conduct or habit, as in the indulgence of degrading appetites; customary deviation in a single respect, or in general, from a right standard, implying a defect of natural character, or the result of training and habits; a harmful custom; immorality; depravity; wickedness; as, a life of vice; the vice of intemperance.
v.
An excursion from the usual track; range; digression; deviation.
n.
Exactness without allowance, deviation, or indulgence; strictness; as, the rigor of criticism; to execute a law with rigor; to enforce moral duties with rigor; -- opposed to lenity.
n.
The person at a geodetic station who has charge of the heliotrope.
n.
One versed in geodesy.
n.
That branch of biological science which treats of monstrosities, malformations, or deviations from the normal type of structure, either in plants or animals.
n.
That branch of the science of geodesy which has to do with the measurement of heights, either absolutely with reference to the sea level, or relatively.
a.
Alt. of Geodetical
a.
Of or pertaining to geodesy; geodetic.
adv.
In a geodetic manner; according to geodesy.
n.
The act of varying; a partial change in the form, position, state, or qualities of a thing; modification; alternation; mutation; diversity; deviation; as, a variation of color in different lights; a variation in size; variation of language.
n.
A variety of trap or basaltic rock, containing small cavities, occupied, wholly or in part, by nodules or geodes of different minerals, esp. agates, quartz, calcite, and the zeolites. When the imbedded minerals are detached or removed by decomposition, it is porous, like lava.
n.
An instrument consisting of a mirror moved by clockwork, by which a sunbeam is made apparently stationary, by being steadily directed to one spot during the whole of its diurnal period; also, a geodetic heliotrope.
a.
Alt. of Geodesical